Foundations for College Math (MBF3C) · Mathematical Models

Find a percent growth rate from an exponential relation

Given a starting and ending value over time, solve A = A0(1 +- r)^t for the annual percent rate r. Unlimited questions, five difficulty levels, and a full worked solution every time, included free with weekly lessons.

Practice this skill Curriculum: MBF3C-MM2, MBF3C-MM3

Try one

A collector bought a limited-edition sneaker for $120.00. After 3 years it is worth $234.38, growing by the same percent every year. What annual percent growth rate does this represent? Round to the nearest whole percent.

A = A0(1 + r)t

Answer: 25

See one solved, step by step

A collector bought a limited-edition sneaker for $700.00. After 2 years it is worth $925.75, growing by the same percent every year. What annual percent growth rate does this represent? Round to the nearest whole percent.

A = A0(1 + r)t
📘 Worked solution
1925.75 = 700(1 + r)2Set up the exponential relation using the starting value, ending value, and the number of years.
21 + r = (925.75 / 700)12 = 1.15Divide both sides by A0, then take the t-th root to undo the exponent.
3r = 0.15 -> 15%Subtract 1 and convert to a percent, rounding to the nearest whole percent.

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